Whilst following up another matter, I came across the following commit to Hugyen's NanoVNA-H4 repository.
Remove R44 from NanoVNA-H4 Rev4.3, this resistor may damage U2 and the battery if the NanoVNA-H4 is not used for a long time and the battery is too low.
Above is an extract from the revised schematic committed, the change highlighted by the red arrow. R44 has been changed from 5.1kΩ to not populated.
The use of the 5.1kΩ resistor is not described / recommmended in the datasheet. Presumably it changes the constant current mode when the NanoVNA is switched on, but it may mess with other battery management settings.
Whilst I have not had problems as mentioned, it is probably because I use it so frequently that the battery has never been fully discharged. It seems from the commit description that the higher current make cause excessive dissipation in the TP4056 battery management chip.
I thought it prudent to check both of the -H4.3 instruments that I own and if necessary remove R44.
Above is a pic of one of the the PCBs with R44 removed. It is an 0603 package, so quite small. I picked it off with SMD desoldering tweezers. The other board was manufactured without R44 installed.
It can be difficult to find documentation on these projects.
It appears that the earlier model (v4.2) used a different battery manager chip (FM5401), soo the issue seems to apply only to v4.3 in the H4 series.